Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

Parallel growing and training of neural networks using output parallelism

In order to find an appropriate architecture for a large-scale real-world application automatically and efficiently, a natural method is to divide the original problem into a set of sub-problems. In this paper, we propose a simple neural network task decomposition method based on output parallelism. By using this method, a problem can be divided flexibly into several sub-problems as chosen, each of which is composed of the whole input vector and a fraction of the output vector. Each module (for one sub-problem) is responsible for producing a fraction of the output vector of the original problem. The hidden structure for the original problem’s output units are decoupled. These modules can be grown and trained in parallel on parallel processing elements. Incorporated with a constructive learning algorithm, our method does not require excessive computation and any prior knowledge concerning decomposition. The feasibility of output parallelism is analyzed and proved. Some benchmarks are implemented to test the validity of this method. Their results show that this method can reduce computational time, increase learning speed and improve generalization accuracy for both classification and regression problems

Incremental learning with respect to new incoming input attributes

Neural networks are generally exposed to a dynamic environment where the training patterns or the input attributes (features) will likely be introduced into the current domain incrementally. This paper considers the situation where a new set of input attributes must be considered and added into the existing neural network. The conventional method is to discard the existing network and redesign one from scratch. This approach wastes the old knowledge and the previous effort. In order to reduce computational time, improve generalization accuracy, and enhance intelligence of the learned models, we present ILIA algorithms (namely ILIA1, ILIA2, ILIA3, ILIA4 and ILIA5) capable of Incremental Learning in terms of Input Attributes. Using the ILIA algorithms, when new input attributes are introduced into the original problem, the existing neural network can be retained and a new sub-network is constructed and trained incrementally. The new sub-network and the old one are merged later to form a new network for the changed problem. In addition, ILIA algorithms have the ability to decide whether the new incoming input attributes are relevant to the output and consistent with the existing input attributes or not and suggest to accept or reject them. Experimental results show that the ILIA algorithms are efficient and effective both for the classification and regression problems

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Connectionist Theory Refinement: Genetically Searching the Space of Network Topologies

An algorithm that learns from a set of examples should ideally be able to exploit the available resources of (a) abundant computing power and (b) domain-specific knowledge to improve its ability to generalize. Connectionist theory-refinement systems, which use background knowledge to select a neural network's topology and initial weights, have proven to be effective at exploiting domain-specific knowledge; however, most do not exploit available computing power. This weakness occurs because they lack the ability to refine the topology of the neural networks they produce, thereby limiting generalization, especially when given impoverished domain theories. We present the REGENT algorithm which uses (a) domain-specific knowledge to help create an initial population of knowledge-based neural networks and (b) genetic operators of crossover and mutation (specifically designed for knowledge-based networks) to continually search for better network topologies. Experiments on three real-world domains indicate that our new algorithm is able to significantly increase generalization compared to a standard connectionist theory-refinement system, as well as our previous algorithm for growing knowledge-based networks.Comment: See http://www.jair.org/ for any accompanying file

Grammars and cellular automata for evolving neural networks architectures

IEEE International Conference on Systems, Man, and Cybernetics. Nashville, TN, 8-11 October 2000The class of feedforward neural networks trained with back-propagation admits a large variety of specific architectures applicable to approximation pattern tasks. Unfortunately, the architecture design is still a human expert job. In recent years, the interest to develop automatic methods to determine the architecture of the feedforward neural network has increased, most of them based on the evolutionary computation paradigm. From this approach, some perspectives can be considered: at one extreme, every connection and node of architecture can be specified in the chromosome representation using binary bits. This kind of representation scheme is called the direct encoding scheme. In order to reduce the length of the genotype and the search space, and to make the problem more scalable, indirect encoding schemes have been introduced. An indirect scheme under a constructive algorithm, on the other hand, starts with a minimal architecture and new levels, neurons and connections are added, step by step, via some sets of rules. The rules and/or some initial conditions are codified into a chromosome of a genetic algorithm. In this work, two indirect constructive encoding schemes based on grammars and cellular automata, respectively, are proposed to find the optimal architecture of a feedforward neural network

Recursive Percentage based Hybrid Pattern Training for Supervised Learning

Supervised learning algorithms, often used to find the I/O relationship in data, have the tendency to be trapped in local optima as opposed to the desirable global optima. In this paper, we discuss the RPHP learning algorithm. The algorithm uses Real Coded Genetic Algorithm based global and local searches to find a set of pseudo global optimal solutions. Each pseudo global optimum is a local optimal solution from the point of view of all the patterns but globally optimal from the point of view of a subset of patterns. Together with RPHP, a Kth nearest neighbor algorithm is used as a second level pattern distributor to solve a test pattern. We also show theoretically the condition under which finding several pseudo global optimal solutions requires a shorter training time than finding a single global optimal solution. As the difficulty of curve fitting problems is easily estimated, we verify the capability of the RPHP algorithm against them and compare the RPHP algorithm with three counterparts to show the benefits of hybrid learning and active recursive subset selection. The RPHP shows a clear superiority in performance. We conclude our paper by identifying possible loopholes in the RPHP algorithm and proposing possible solutions